Question

The electric supply line in house works at 220 volts. The amplitude of emf will be
(A) 220 volts
(B) 311 volts
(C) 110 volts
(D) 440 volts

Answer 1

Hint : Electric supply line in houses supply alternate current electricity. The voltage or emf ratings of AC electricity are given as root mean square values.

Formula used: In this solution we will be using the following formula;
 $ {V_{rms}} = \dfrac{{{V_p}}}{{\sqrt 2 }} $ where $ {V_{rms}} $ is the root mean square value of voltage or emf, and $ {V_p} $ is the peak value or amplitude of the voltage.

Complete step by step answer
We are told that the electric supply line works at a particular emf rating, the amplitude of the emf is to be determined.
To solve this, one must note that the electric supply line in a house is alternate current electricity, and the ratings of ac electricity are given by their root mean square (rms) value. Hence, the 220 volts given in the question is the root mean square value of the instantaneous voltage of the ac electricity.
Thus, to calculate the amplitude of the emf, we recall the formula
 $ {V_{rms}} = \dfrac{{{V_p}}}{{\sqrt 2 }} $ where $ {V_{rms}} $ is the root mean square value of voltage or emf, and $ {V_p} $ is the peak value or amplitude of the voltage.
Making the peak voltage $ {V_p} $ the subject of the formula by multiplying both sides by $ \sqrt 2 $ , we have
 $ {V_p} = {V_{rms}}\sqrt 2 $
Hence, inserting the value of the rms given we have
 $ {V_p} = 220\sqrt 2 $
 $ \Rightarrow {V_p} = 311{\text{ volt}} $
Hence, the correct option is B.

Note
For clarity, note that there is a very slight and often discarded difference between peak voltage and the amplitude of the emf. Peak voltage is the maximum voltage obtained by the instantaneous values of the electricity, while the amplitude is the difference between the peak voltage and the line which divides the wave into two halves. In simple terms, peak voltage is the point while amplitude is the “distance” or “height” above the x axis.